Why cut them into triangles at all?? Use the "thangles" method of sewing them into HST by matching two strips together and sewing your seam THEN cutting.
With this method your edges will be biased
http://www.quiltingboard.com/t-37915-1.htm
With this method you bias edge will be encased in the seam, I prefer this.
http://www.quiltingandwhatnot.ca/Hal...-Triangle.html
You will have to cut the pattern pieces into strips to match your strips widths. The .pdf files are made for 8 1/2 x 11 sheets of paper. I don't know how wide your strips are.